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brairtrainer

Dragcave Maths

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Sufficient number of incubates has been previously worked out; for a gold trophy it is 49 smile.gif

Beat me to it. 7 eggs at a time, 14 day cooldown, 2 days for an incubated egg to grow up. 49 Reds.

Edited by Engiype

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Okay, so the big question of this thread...

 

How long would it take for ONE person to complete a project on this scale, assuming EVERYTHING worked out as planned and as quickly as possible?

Also, how many red dragons would be required?

 

For the sake of THIS math, I'm assuming the user has a gold trophy and so can hold 7 eggs at a time.

 

 

First, the red dragon math...

A red dragon can incubate only once every 14 days.

An egg with incubate can be hatched within 2 days.

A user with 7 egg spots can grow 7 eggs every 2 days.

A user hatching eggs every two days can hatch 7 dragons in that 14 day timeframe.

 

Hence, the maximum number of red dragons a user will require is 7 * 7 = 49 red dragons.

Once a user has 49 red dragons they will always have an incubate available.

(This, of course, is assuming that the user keeps each egg until it hatches. An additional red dragon will be required for every abandoned incubated dragon).

 

Double checking against the 21-growing things limit...

Day 1 - 7 eggs = 7 total

Day 2 - 7 eggs = 7 total

Day 3 - 7 eggs and 7 hatchlings = 14 total

Day 4 - 7 eggs and 7 hatchlings = 14 total

Day 5 - 7 eggs and 14 hatchlings = 21 total

Day 6 - 7 eggs and 7 hatchlings = 14 total

Day 7 - 7 eggs and 14 hatchlings = 21 total

 

So someone who only picks up eggs (all on the same day), incubates everything, and keeps repeating this cycle whenever the eggs hatch will reach but not exceed their scroll limit for growing things on day 5 and then every other day thereafter.

 

So 7 eggs every 2 days is the upper limit and can be used for successful calculations for the project.

 

 

So, on to the next calculation...

EDIT: Which I'm not doing today but I will give you this. xd.png

 

2^(100-n) is the number of eggs per generation, where n = the generation.

 

2^(99)+2^(98)+2^(97)+2^(96)+...+2^0 = the number of dragons necessary to complete a non-inbred 100-generation even-gen project.

 

365/2 * 7 = 1277.5 dragons a user can hatch every year. This is with incubate.

For growing every year, the number drops slightly to ~1268.2 (This number is merely an estimate but it should be close. I subtracted the 7 most recently hatched eggs plus subtracted another 7/3 to compensate for the third day of hatchling-dom for another seven).

 

That said, for the sake of calculations the 1277.5 per year number would be more accurate, since this would be a multi-year project, and the 1277.5 would compensate for the "rolling" nature of raising dragons. The calculations should not expect the user to stop collecting dragons and let their scroll go empty before starting again the next year.

 

That said, using a straight year calculation does not account for the final 3 generations, where the 100th generation will have only one dragon at a time, the 99th generation will have 2 dragons, the 98th generation will have 4. These do not take full advantage of the 7-egg scroll limit, since there cannot be more dragons included in that generation.

Edited by SolarCat

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We're already working on this one, and we should have an answer soon. I'll edit this post when we've confirmed it.

Ok, thanks smile.gif

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You can raise roughly 851 dragons in a year without incubate, and 1277 without tongue.gif

Makes incubate seem a lot more worth while...

 

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This thread is making my head hurt, but it is rather interesting. And I love how "What is the square root of a Purple dragon?" actually has an answer. xd.pngs

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I hate to steal Brair's question here, but it's been a while, she didn't respond in the IRC, and I have a solution.

 

The answer to the "how long would it take" question (for one user) is now posted on the first page, in the post I had said I would edit when we got the answer.

 

However I will repeat it here as well for those who don't feel like looking back.

 

And if by some miracle, it becomes possible to create a 100 EG, how long will it take?

So lets assume a single player decided to take this epic adventure all by himself.

Lets assume the following variables are true;

- Sufficient number of Incubates (reds)

- NO refusals

- Dragons always give egg

- Eggs gender correctly every time.

 

How long would it take for a player to get to gen 100?

 

 

Okay, here's my solution.

 

So if we have 1267650600228229401496703205376 CB dragons, we'll have to breed 633825300114114700748351602688 (half of 1267650600228229401496703205376) pairs the first generation to produce 633825300114114700748351602688 eggs. The next generation will be half of that, and so on, until we're down to one dragon.

 

So we need to find out how many pairs we'd need to breed total.

633825300114114700748351602688 + 633825300114114700748351602688/2 + 633825300114114700748351602688/4 ... + 4 + 2 + 1 = ?

 

There's a handy trick, thankfully, for adding up powers of 2. Say you want to add up the powers of 2, up to 2^5. 1 (or 2^0) + 2 + 4 + 8 + 16 + 32 = 63. The shortcut is to do (2^(5+1))-1, which is also 63. So the general formula is (2^(n+1)) - 1. Now we can quickly calculate that we will be breeding 1267650600228229401496703205375 pairs total.

 

Now on to the trickier part. (Oh yes, there's a trickier part.) EGG LIMITS. Since we're starting out with 1267650600228229401496703205376 dragons, we obviously have a gold trophy. So we can deal with 7 pairs at a time before we're egg locked. Then we have to wait 3 days for those eggs to hatch and we can do 7 more.

 

Now towards the end of the line there are fewer dragons we have in the youngest generation than egg slots. What I mean is that when we get to the generation where we have to breed 4 pairs, we can't do 7 at a time any more, because we have to wait for the newest ones to grow up to adulthood (rather than 3 days to hatch) before we can breed them.

 

I'll go to the trouble of dealing with these few pesky generations first. From the generation where we have to breed 8 pairs on, it will take 33 days to breed the rest of the dragons.

 

Now we only have 1267650600228229401496703205360 pairs to go! The rest of these are simple to do. Group of 7, then wait 3 days to unlock. Group of 7, wait 3 days. And so on.

 

Between the easy pairs and the pesky ones I did for you, we get a final answer of 543278828669241172070015659473 days.

 

Or 1488435147039016909780864820.474 years.

Or 1488435147039016909780864.820474 millenia.

Or 106316796217072636.41291891574814 times the age of the universe (14 billion years).

 

What's that, you say? You want infinite Incubates?

 

Well that certainly makes it go faster. Using the same technique as before, we get a final answer of:

362185885779494114713343772988 days.

Or 992290098026011273187243213.66575 years.

Or 992290098026011273187243.21366575 millenia.

Or 70877864144715090.941945943833268 times the age of the universe.

 

It'll be a while.

Edited by Engiype

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sorry for that guys, but I didn't expect everyone taking a jumping off point and I got called away for a very long time D: I will be here to keep answering questions though biggrin.gif

 

edit: also I'm a she

Edited by brairtrainer

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How many times could a member post in a year if you assumed they posted exactly every 30 second (or is flood control 60? Whatever it is) without rest or sleep?

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How many CB eggs could one person catch in one day assuming they had a gold trophy and they abandoned each egg they caught as soon as they could?

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Oh my god, you guys. xd.png

 

I actually did wonder how many dragons it would take once (I had seen PonyTales' pink PB project and was like "Oooh! Impressive! I wonder...") but never bothered to figure it out. x3

 

... You crusher of dreams. =P

Heh heh I just finished collecting 512 CB pinks (I've been really slow!) and I started in '09 unsure.gif

 

1267650600228229401496703205376 CBs? *faints*

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How many times could a member post in a year if you assumed they posted exactly every 30 second (or is flood control 60? Whatever it is) without rest or sleep?

In a typical (non-leap) calendar year (as opposed to a true solar year), there are 525600 minutes.

 

1 * 60 min/hr * 24 hr/d * 365 d/y = 525600 min/y

 

30 seconds are just half a minute, so the final answer is 525600 * 2, or 1051200.

 

This of course doesn't take into account milliseconds of lag that would add up over the course of the year.

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How many CB eggs could one person catch in one day assuming they had a gold trophy and they abandoned each egg they caught as soon as they could?

Assuming they had all 7 slots open at the start, first they would catch 7 eggs. Then there would be a five hour wait until they could dump them all and get 7 more.

 

In a day, this cycle can repeat completely four times, making the answer 28 eggs caught and dumped, and 35 if you count the 7 that the person is holding at the end of the day, which can be dumped in just one more hour.

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Approximately how many threads go through the help forum in one year?

 

I leave all research to you. It'll be more fun for you that way.

Before we start, I'm just going to mention that for this solution, I did not count the "Tiny Little Questions" thread. It could arguably be counted as many different topics in one thread, since it is, after all, a bunch of tiny little topics. I also omitted it for a reason I'll reveal later.

 

I started solving this one way, then tried a different way and got a better answer.

 

There's a neat little feature on the forums that I think very few people use. At the bottom of any section, there are three boxes. You can choose how far back you want it to display (1 week, 90 days, etc.) and how to sort them. To solve this, I figured I'd start by viewing all threads in Help sorted by Topic Start Date, going back 15 days. There were 81 results, so if this rate was constant for the entire year, the answer would be 1971 threads in a year.

 

user posted image

 

Then I decided to check my work.

 

I sorted the Help section differently--still by Topic Start Date, but this time I had it display all threads from "the beginning." I got 181 results, which surprised me because the Help section has been around for years, while if threads were created at the rate I had calulated earlier, 181 threads would be only a little over a month's worth. Clearly something was off.

 

user posted image

 

I checked the date of the OP of the oldest thread that showed up in this latest search. (Actually the oldest thread was TLQ, but yeah.) It was dated January 17th, 2013. Today is February 26th, so that means that what was supposedly the oldest thread in Help was just 40 days old! The most likely explanation for this is that old threads probably get deleted every so often to keep Help clean.

 

So let's do the math here. 181 threads in 40 days would mean 1651.625 threads per year. That's lower than the first number, but it's still pretty close.

 

The larger sample size is usually more accurate, so I'm going to go ahead and announce 1652 (to the nearest whole) as my final answer here.

 

 

Note:

 

By the way, this is also why I didn't include the TLQ thread--it was posted in 2010, and there's a huge gap between that and the second oldest thread, which was from just 40 days ago. This is due to threads being cleaned out since it was created, but TLQ (still being a legitimate topic) sticking around. So TLQ is a huge outlier and it would have tremendously thrown off the results if I had used it as the oldest thread.

Edited by Engiype

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It's so much fun reading all the maths. I don't have the patience to do it but I wish I did.

 

Say you have a pair of breedable dragons on June 1, 2006, and breeding is available as an action. You breed each offspring with a caveborn dragon. What's the longest possible lineage dragon, in number of generations, that you can have on February 26, 2013, assuming that you bred them as soon as they matured, there are no rejects, you always have the correct-gendered pairs, and no BSAs are used?

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the answer to that is 814 breedings meaning that many generations O.O

 

I figured it out by first taking the amount of dragons that can be raised in a week (2 2/3) from the line and multiplying that by how many weeks in a year (52). Then I multiplied that by 6 to get us to June 1, 2012, then took the amount of weeks it would take to get us close to but not over February 26, 2013. Because June 1, 2006 was on a Thursday you did not end up with a breeding on February.

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This is really interesting! I hadn't associated DC with math before.

 

What's the approximate probability of summoning a GoN? And if a person summoned every time when the action was available, how long would it take them, on average?

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This is really interesting! I hadn't associated DC with math before.

 

What's the approximate probability of summoning a GoN? And if a person summoned every time when the action was available, how long would it take them, on average?

I don't think anything can be said on this other than "a reasonable amount".

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This is really interesting! I hadn't associated DC with math before.

 

What's the approximate probability of summoning a GoN? And if a person summoned every time when the action was available, how long would it take them, on average?

In order to do this I'd need to know what was the chance of summoning with one pair of trios, and how much the next sets increased the chance. I think that right now that falls under reverse engineering, and unless TJ himself comes and gives us the information we can't figure that out. Sorry sad.gif

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What's the approximate probability of summoning a GoN? And if a person summoned every time when the action was available, how long would it take them, on average?

For simplicity's sake, I'm going to assume we have only one set of Trios.

 

Well, we don't know the exact probability of summoning a GoN, but the Dragon Cave Wiki estimates it at about this:

There is rumored to be a 0.5%-11% chance for a summoning to be successful.

That's a pretty wide range. A really wide range, actually. How wide exactly? Well some quick math tells us that we could get a GoN in anywhere from about 9 to 200 summons. Multiply that by a 30-day cool down and we now know that getting a GoN would take (on average) anywhere from 270 to 6000 days.

 

Like I said, that's a really wide range. So wide that the best answer to this question is simply "a while."

 

Good luck, all you summoners!

Edited by Engiype

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It's fun reading these answers, but mind boggling for a totally non math orientated person like myself.

 

My question is this:

 

Assuming a newly registered user takes no time off and catches a new random dragon, without waiting, each time they have a space, all their eggs hatch in optimum time, and they use no BSAs, how long will it take them to earn a gold trophy?

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Assuming a newly registered user takes no time off and catches a new random dragon, without waiting, each time they have a space, all their eggs hatch in optimum time, and they use no BSAs, how long will it take them to earn a gold trophy?

So how this would work is the user would catch a group of however many dragons they were able, then wait 3 days for them to hatch, and do it again. I worked out how many times they'd have to do this before moving up a trophy level.

 

No trophy: 13 reps, 39 days, 52 dragons caught while on that trophy level

Bronze trophy: 30 reps, 90 days, 150 dragons caught while on that trophy level

Silver trophy: 50 reps, 150 days, 300 dragons caught while on that trophy level

 

Total: 279 days, and 502 dragons to show for it.

 

The reason the "no trophy" level needs 52 dragons before moving up to bronze is because at that point, dragons are caught in groups of 4. They all hatch and grow up at the same time, so to put the user over 50 dragons, the latest set of 4 dragons would grow up at exactly the same time, bumping the user from 48 to 52 adult dragons. The "no trophy" level is the only one for which this happens.

Edited by Engiype

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The question about the 100th EG lineage got me wondering: How long would it take to create a 100th gen clean stairstep and how many dragons would you need? For a 100th gen inbred one?

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The question about the 100th EG lineage got me wondering: How long would it take to create a 100th gen clean stairstep and how many dragons would you need? For a 100th gen inbred one?

For a 100th gen clean stair step you'd need two to start, then 99 cbs, bringing you to 101 cbs +99 bred ones (since bred ones start at gen 1) so overall the dragons would be 200

 

For a 100 gen inbred one assuming you're using the mother or father as the cb you have 99 bred dragons + the mother + the father =101 dragons

 

EDIT: this is much more doable, so you can have a 100 gen dragon, but he can't be evengen

Edited by brairtrainer

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